# 특이값 분해

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## 노트

1. a numeric or complex matrix whose SVD decomposition is to be computed.[1]
2. The singular value decomposition plays an important role in many statistical techniques.[1]
3. SVD can be used to find a generalized inverse matrix.[2]
4. Then, using SVD, we can essentially compress the image.[2]
5. PCA can be achieved using SVD.[2]
6. Multi-dimensional scaling can also be achieved using SVD.[2]
7. Calculating the SVD consists of finding the eigenvalues and eigenvectors of AAT and ATA.[3]
8. The final section works out a complete program that uses SVD in a machine-learning context.[4]
9. SVD is known under many different names.[4]
10. We have already seen in Equation (6) how an SVD with a reduced number of singular values can closely approximate a matrix.[4]
11. Because n is large, however, the algorithm takes too long or is unstable, so we want to reduce the number of variables using SVD.[4]
12. In this paper, we modify a classical downdating SVD algorithm and reduce its complexity significantly.[5]
13. Perhaps the most known and widely used matrix decomposition method is the Singular-Value Decomposition, or SVD.[6]
14. All matrices have an SVD, which makes it more stable than other methods, such as the eigendecomposition.[6]
15. The SVD is calculated via iterative numerical methods.[6]
16. The singular value decomposition (SVD) provides another way to factorize a matrix, into singular vectors and singular values.[6]
17. In this article, I will try to explain the mathematical intuition behind SVD and its geometrical meaning.[7]
18. To understand SVD we need to first understand the Eigenvalue Decomposition of a matrix.[7]
19. Before talking about SVD, we should find a way to calculate the stretching directions for a non-symmetric matrix.[7]
20. Now we can summarize an important result which forms the backbone of the SVD method.[7]
21. The SVD also captures indirect connections.[8]
22. The transaction item matrix is centered, scaled, and divided by nTran minus 1 before the singular value decomposition is carried out.[8]
23. The SVD implementation takes advantage of the sparsity of the transaction item matrix.[8]
24. Otherwise, it can be recast as an SVD by moving the phase of each σ i to either its corresponding V i or U i .[9]
25. The singular value decomposition can be used for computing the pseudoinverse of a matrix.[9]
26. The SVD can be thought of as decomposing a matrix into a weighted, ordered sum of separable matrices.[9]
27. The SVD can be used to find the decomposition of an image processing filter into separable horizontal and vertical filters.[9]
28. SVD allows us to extract and untangle information.[10]
30. SVD gives you the whole nine-yard of diagonalizing a matrix into special matrices that are easy to manipulate and to analyze.[10]
31. Let’s introduce some terms that frequently used in SVD.[10]
32. Here the SVD is used to perform a pseudoinverse of an otherwise ill-conditioned operator.[11]
33. For image processing and large scale inverse problems this requires the SVD of a large matrix.[11]
34. SVD is suited to regularisation because one has access to the singular values of the operator.[11]
35. Another feature of SVD is that it reveals the rank of the operator, useful in many imaging algorithms and signal processing applications.[11]
36. The most fundamental dimension reduction method is called the singular value decomposition or SVD.[12]
37. The SVD is a matrix decomposition, but it is not tied to any particular statistical method.[12]
38. SVD and Signal Processing II: Algorithms, Analysis and Applications, edited by R. Vaccaro, Elsevier Science Publishers, North Holland, 1991.[13]
39. x a numeric or complex matrix whose SVD decomposition is to be computed.[14]
40. There are a few caveats one should be aware of before computing the SVD of a set of data.[15]
41. The svd function computes the singular value decomposition of the SST dataset weighted over the cosine of the latitude.[15]
42. A weight term, however, is not necessary to complete the SVD analysis.[15]
43. This will remove the normalized eigenvector variable selection and return you to the SVD page.[15]
44. The SVD represents the essential geometry of a linear transformation.[16]
45. Recall that the diagonal elements of the Σ matrix (called the singular values) in the SVD are computed in decreasing order.[16]
46. In SAS, you can use the SVD subroutine in SAS/IML software to compute the singular value decomposition of any matrix.[16]
47. To save memory, SAS/IML computes a "thin SVD" (or "economical SVD"), which means that the U matrix is an n x p matrix.[16]
48. SVD produces two sets of orthonormal bases (U and V).[17]
49. The singular value decomposition (SVD) is a generalization of the algorithm we used in the motivational section.[18]
50. As in the example, the SVD provides a transformation of the original data.[18]
51. It is not immediately obvious how incredibly useful the SVD can be, so let’s consider some examples.[18]
52. Let’s compute the SVD on the gene expression table we have been working with.[18]
53. This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data.[19]
54. Gene expression data are currently rather noisy, and SVD can detect and extract small signals from noisy data.[19]
55. SVD and PCA are common techniques for analysis of multivariate data, and gene expression data are well suited to analysis using SVD/PCA.[19]
56. In section 1, the SVD is defined, with associations to other methods described.[19]